Wrong "probability of meeting" intuition

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This is a follow-up to this question

Can someone help me understand why the following geometric intuition is wrong? Graph with geometric intuition

The setup is the same, where we let x and y be the arrival times of A and B. Then, we condition on the arrival time of A: whenever A arrives, for them to meet, B has to arrive at most 10 minutes later. Therefore, the region is bounded by the equations

$$ x = y $$ $$ x + 10 = y $$ $$ 0 ≤ x ≤ 60 $$ $$ 0 ≤ y ≤ 60 $$

I can't find the flaw in this, but it doesn’t give the same result as the linked answer.